An X-ray microscope has a mirror for gathering light. This mirror is indicated by M in FIG. 1(a) and has a hyperboloid R1 and a paraboloid R2. In order to form this mirror M by molding, a molding die having the same hyperboloid R1 and paraboloid R2 as those of the mirror M as shown in FIG. 1(b) is employed. This die is machined by a machine tool such as a lathe. In order to efficiently gather feeble x-rays coming from outer space, it is necessary to machine this die with high profile accuracy and with small surface roughness.
In such accurate machining, it is necessary to determine the profile of the workpiece machined by the machine tool at an accuracy of the order of 0.1 .mu.m. However, when the above-described die is used, the diameter varies by several millimeters with axial position and, therefore, it is impossible to determine the profile at the required accuracy. That is, with the prior art measuring apparatus, it has been impossible to determine the profile of an object whose diameter changes greatly, at an accuracy of the order of 0.1 .mu.m.
Where the profile of a workpiece is determined, a measuring instrument is installed outside a machine tool. The workpiece is removed from the machine tool. Then, the profile is determined. A correcting machining operation is carried out according to the result of the measurement. In this method, the machined workpiece is needed to be shifted from the machine tool to the measuring instrument for the determination of the profile. To machine the workpiece again, it is required to be returned to the machine tool. In this way, the efficiency of the operation is low. Also, when the workpiece is mounted again on the machine tool, the position at which the workpiece is installed deviates from the original position. This makes it impossible to accurately correct the contour of the workpiece that has been once machined.
In an attempt to eliminate the foregoing problems, the present inventor has contemplated a method of determining the profile of a workpiece while it is held on a machine tool. In this method, a detector for detecting the radial position of the outer periphery of a workpiece is mounted on one side of the axis of rotation of the workpiece. The spindle head which holds and rotates the workpiece is moved parallel to the axis of rotation of the workpiece. The manner in which the radius of the workpiece varies with axial position is known from the output signal from the detector. The profile of the workpiece is determined from the relation of the radius to the axial position.
In this method, the workpiece is displaced radially while the spindle head is moving because of an error introduced in the straightness of the table that supports the spindle head. As a result, the output signal from the detector involves the straightness error. Hence it is impossible to accurately measure the contour of the workpiece.